Course overview

1. Course overview Digital Image Synthesis Yung-Yu Chuang 9/21/2006 with slides by Mario Costa Sousa, Pat Hanrahan and Revi Ramamoorthi

2. Logistics • Meeting time: 1:30pm-4:20pm, Thursday • Classroom: CSIE Room 111 • Instructor: Yung-Yu Chuang (cyy@csie.ntu.edu.tw) • TA: Shan-Yung Yang • Webpage: http://www.csie.ntu.edu.tw/~cyy/rendering id/password • Forum: http://www.cmlab.csie.ntu.edu.tw/~cyy/forum/viewforum.php?f=8 • Mailing list: rendering@cmlab.csie.ntu.edu.tw Please subscribe via https://cmlmail.csie.ntu.edu.tw/mailman/listinfo/rendering/

3. Prerequisites • C++ program experience is required. • Basic knowledge on algorithm and data structure is essential. • Knowledge on linear algebra, probability and compilers is a plus. • Though not required, it is recommended that you have background knowledge on computer graphics.

4. Requirements (subject to change) • 2 programming assignments (40%) • Presentation (15%) (course will alternate between lectures and paper presentations) • Class participation (5%) • Final project (40%)

5. Textbook Physically Based Rendering from Theory to Implementation, by Matt Pharr and Greg Humphreys • Authors have a lot of experience on ray tracing • Complete (educational) code, more concrete • Plug-in architecture, easy for experiments and extension • Has been usedin some papers

6. Literate programming • A programming paradigm proposed by Knuth when he was developing Tex. • Programs should be written more for people’s consumption than for computers’ consumption. • The whole book is a long literate program. That is, when you read the book, you also read a complete program.

7. Features • Mix prose with source: description of the code is as important as the code itself • Allow presenting the code to the reader in a different order than to the compiler • Easy to make index • Traditional text comments are usually not enough, especially for graphics • This decomposition lets us present code a few lines at a time, making it easier to understand. • It looks more like pseudo code.

8. LP example @\section{Selection Sort: An Example for LP} We use {\it selection sort} to illustrate the concept of {it literate programming}. Selection sort is one of the simplest sorting algorithms. It first find the smallest element in the array and exchange it with the element in the first position, then find the second smallest element and exchange it the element in the second position, and continue in this way until the entire array is sorted. The following code implement the procedure for selection sort assuming an external array [[a]]. <<*>>= <<external variables>> void selection_sort(int n) { <<init local variables>> for (int i=0; i<n-1; i++) { <<find minimum after the ith element>> <<swap current and minimum>> } }

9. LP example <<find minimum after the ith element>>= min=i; for (int j=i+1; j<n; j++) { if (a[j]<a[min]) min=j; } <<init local variables>>= int min; @ To swap two variables, we need a temporary variable [[t]] which is declared at the beginning of the procedure. <<init local variables>>= int t; @ Thus, we can use [[t]] to preserve the value of [[a[min]] so that the swap operation works correctly. <<swap current and minimum>>= t=a[min]; a[min]=a[i]; a[i]=t; <<external variables>>= int *a;

10. LP example (tangle) int *a; void selection_sort(int n) { int min; int t; for (int i=0; i<n-1; i++) { min=i; for (int j=i+1; j<n; j++) { if (a[j]<a[min]) min=j; } t=a[min]; a[min]=a[i]; a[i]=t; } }

11. LP example (weave)

12. Reference books

13. Reference • SIGGRAPH proceedings • Proceedings of Eurographics Symposium on Rendering • Eurographics proceedings

14. Image synthesis (Rendering) • Create a 2D picture of a 3D world

15. Applications • Movies • Interactive entertainment • Industrial design • Architecture • Culture heritage

16. Animation production pipeline storyboard story text treatment storyreal look and feel voice

17. Animation production pipeline animation layout modeling/articulation shading/lighting rendering final touch

18. Computer graphics modeling rendering animation

23. The goal of this course • Realistic rendering • First part: physically based rendering • Second part: real-time high quality rendering

24. Physically-based rendering uses physics to simulate the interaction between matter and light, realism is the primary goal

25. Realism • Shadows • Reflections (Mirrors) • Transparency • Interreflections • Detail (Textures…) • Complex Illumination • Realistic Materials • And many more

26. Other types of rendering • Non-photorealistic rendering • Image-based rendering • Point-based rendering • Volume rendering • Perceptual-based rendering • Artistic rendering

27. Pinhole camera

28. Introduction to ray tracing

29. Ray Casting (Appel, 1968)

30. Ray Casting (Appel, 1968)

31. Ray Casting (Appel, 1968)

32. Ray Casting (Appel, 1968)

33. Ray Casting (Appel, 1968) direct illumination

34. Whitted ray tracing algorithm

35. Whitted ray tracing algorithm

36. Shading

37. Ray tree

38. Recursive ray tracing (Whitted, 1980)

39. Components of a ray tracer • Cameras • Films • Lights • Ray-object intersection • Visibility • Surface scattering • Recursive ray tracing

40. Minimal ray tracer • Minimal ray tracer contest on comp.graphics, 1987 • Write the shortest Whitted-style ray tracer in C with the minimum number of tokens. The scene is consisted of spheres. (specular reflection and refraction, shadows) • Winner: 916 tokens • Cheater: 66 tokens (hide source in a string) • Almost all entries have six modules: main, trace, intersect-sphere, vector-normalize, vector-add, dot-product.

41. Minimal ray tracer (Heckbert 1994)

42. Let’s trace code • Pretty much the same as the format of the textbook, illustrating concepts by showing working source code • Ray tracer usually contains tricks (for efficiency, here, for reducing tokens) • The basic frameworks are the same

43. Minimal ray tracer (scene description) • 888 tokens /* ray.h for test1, first test scene */ #define DEPTH 3 /* max ray tree depth */ #define SIZE 32 /* resolution of picture in x and y */ #define AOV 25 /* total angle of view in degrees */ #define NSPHERE 5 /* number of spheres */ AMBIENT = {.02, .02, .02}; /* ambient light color */ /* sphere: x y z r g b rad kd ks kt kl ir */ SPHERE = { 0., 6., .5, 1., 1., 1., .9, .05, .2, .85, 0., 1.7, -1., 8., -.5, 1., .5, .2, 1., .7, .3, 0., .05, 1.2, 1., 8., -.5, .1, .8, .8, 1., .3, .7, 0., 0., 1.2, 3., -6., 15., 1., .8, 1., 7., 0., 0., 0., .6, 1.5, -3., -3., 12., .8, 1., 1., 5., 0., 0., 0., .5, 1.5, }; refraction index diffuse radius reflection emitting

44. Minimal ray tracer (geometry) /* minimal ray tracer, hybrid version - 888 tokens * Paul Heckbert, ucbvax!pixar!ph, 13 Jun 87 * Using tricks from Darwyn Peachey and Joe Cychosz. */ #define TOL 1e-7 #define AMBIENT vec U, black, amb #define SPHERE struct sphere {vec cen, color; \ double rad, kd, ks, kt, kl, ir} \ *s, *best, sph[] typedef struct {double x, y, z} vec; #include "ray.h" yx; double u, b, tmin, sqrt(), tan();

45. Minimal ray tracer (geometry utilities) double vdot(A, B) vec A, B; { return A.x*B.x + A.y*B.y + A.z*B.z; } vec vcomb(a, A, B) /* aA+B */ double a; vec A, B; { B.x += a*A.x; B.y += a*A.y; B.z += a*A.z; return B; } vec vunit(A) vec A; { return vcomb(1./sqrt(vdot(A, A)), A, black); }

46. Minimal ray tracer (cameras/films) main() { printf("%d %d\n", SIZE, SIZE); while (yx<SIZE*SIZE) U.x = yx%SIZE-SIZE/2, U.z = SIZE/2-yx++/SIZE, /* 360/PI~=114 */ U.y = SIZE/2/tan(AOV/114.5915590261), U = vcomb(255.,trace(DEPTH,black,vunit(U)),black), /* yowsa! non-portable! */ printf("%.0f %.0f %.0f\n", U); }

47. D -u r U C P b Minimal ray tracer (ray-object intersection) struct sphere *intersect(P, D) vec P, D; { best = 0; tmin = 1e30; s = sph+NSPHERE; while (s-->sph) b = vdot(D, U = vcomb(-1., P, s->cen)), u = b*b-vdot(U, U)+s->rad*s->rad, u = u>0 ? sqrt(u) : 1e31, u = b-u>TOL ? b-u : b+u, tmin = u>=TOL && u<tmin ? best = s, u : tmin; return best; }

48. b u U C Minimal ray tracer (ray-object intersection) struct sphere *intersect(P, D) vec P, D; { best = 0; tmin = 1e30; s = sph+NSPHERE; while (s-->sph) b = vdot(D, U = vcomb(-1., P, s->cen)), u = b*b-vdot(U, U)+s->rad*s->rad, u = u>0 ? sqrt(u) : 1e31, u = b-u>TOL ? b-u : b+u, tmin = u>=TOL && u<tmin ? best = s, u : tmin; return best; } D r P

49. N N C Minimal ray tracer (recursive ray tracing) vec trace(level, P, D) vec P, D; { double d, eta, e; vec N, color; struct sphere *s, *l; if (!level--) return black; if (s = intersect(P, D)); else return amb; color = amb; eta = s->ir; d = -vdot(D, N = vunit(vcomb(-1.,P=vcomb(tmin,D,P),s->cen))); if (d<0) /* go into sphere */ N = vcomb(-1., N, black), eta = 1/eta, d = -d; D P η

50. Minimal ray tracer (recursive ray tracing) l = sph+NSPHERE; while (l-->sph) if ((e=l->kl*vdot(N,U=vunit(vcomb(-1.,P,l->cen))))> 0 && intersect(P, U)==l) color = vcomb(e, l->color, color); U = s->color; color.x *= U.x; color.y *= U.y; color.z *= U.z; e = 1-eta*eta*(1-d*d); /* the following is non-portable: we assume right to left arg evaluation. (use U before call to trace, which modifies U)*/ return vcomb(s->kt, e>0 ? trace(level, P, vcomb(eta,D,vcomb(eta*d-sqrt(e), N, black))) : black, vcomb(s->ks, trace(level, P, vcomb(2*d, N, D)), vcomb(s->kd, color, vcomb(s->kl, U, black)))); }